状态空间虚功原理的动荷载识别方法

Dynamic Force Identification Method of State Space Virtual Work Principle

提出一种在状态空间中用虚功原理识别结构外荷载的荷载识别方法。首先,将结构运动方程用状态方程表示,降低方程的阶数;其次,用虚功原理将状态方程转化为等效积分方程;然后,对等效积分方程采用分部积分,减少方程中结构响应类型,同时,对结构响应的求导转换到对已知的虚位移函数求导;最后,用移动最小二乘法将结构位移响应、速度响应及外荷载进行参数化表达,荷载识别问题转化为待识别参数的求解,微分方程反问题转换为代数方程的求解。通过数值仿真表明:采用结构位移响应,且采集的位移响应数量不少于待识别荷载数,信号信噪比不低于30的条件下,该方法对三角波荷载、谐波荷载及随机动荷载均能准确识别。

A load identification method for identifying external structural load in state space with virtual work principle is presented. First,the structural motion equation was expressed in terms of the state equation to reduce the order of the equation. Second,the state equation was transformed into its equivalent integral equation based on the virtual work principle. Then,integration by parts was performed on the equivalent integral equation to reduce the types of structural responses presented in the equation. At the same time,the derivations of structural response components were transformed into that of the known virtual displacement functions. At last,with the moving least square method,the structural displacement response,speed response,and external loads were converted into its corresponding parametric representations,taking the load parameters as those that needed solving,and the inverse problem of the differential equation as the means to solve the algebraic equation. The numerical simulation indicates that： when the structural displacement response is used,the number of displacement responses collected is no less than the number of loads to be identified; when the signal-to-noise is ≥ 30,such method may precisely identify triangular wave loads,harmonic wave loads,and random dynamic loads.